A dialogue between an eleven-year-old prodigy
and his mentor leads to a conjecture on the achievements of Ashkenazic
Jews, and an estimate of the mean IQ of the Nobel laureates.

Mentor.
Welcome. Please sit down.

Prodigy.
Thank you. As always I look forward to our meetings.

Mentor.
At our last conversation, we talked about the accomplishments of that extraordinary
people, the Ashkenazic Jews. We needed some data to continue. Were you
able to find some?

Prodigy.
A lot of not very useful stuff is out there, mostly accounts of Who's Who
in Jewry. As you predicted, however, I was able to get what we needed from
Arthur Hu. Hu's
website is a veritable encyclopedia of ethnicity. Visiting it is an
experience. He lists the percentage of Jews in 28 categories of achievement.
It is apparent that the Jews represented in the data are mostly American,
and consequently Ashkenazim. I brought the data for us to look at. It's
in the form of a table.

% Jewish

% Jewish

100%

CA Senators 1996

17%

Nobel Physiology and
Medicine

85%

College age Jews in
college

16%

Time Most Important
25

76%

Most influential intellectuals

(Alan Dershowitz)

15%

MacArthur "Genius" Awards
1981-97

60%

Yale Grad students

15%

Time 20 20th Century
Inventors

60%

Top Hollywood positions

(60 min)

15%

USA Today College Academic
Team

40%

Lawyers at best NY and
DC law firms

14%

Clinton Cabinet 1997

20-30%

Westinghouse Science
Prize

11%

Nobel Physics Prize

30%

Faculty at elite colleges

10%

Pulitzer 1997

30%

Supreme Court Law Clerks

10%

US Senate

27%

Ivy League Survey

10%

US college faculty

26%

US Law Professors

(Volokh UCLA)

7.7%

Corporate Boards

25%

ACM Turing Award

7%

Forbes HiTech 100 1997

23%

Wealthiest Americans

3.0%

US Voters 1996

23%

Top 100 wealthy Canadians

2.0%

US Population

17%

Boston Symphony Strings

0.25%

World Population

Mentor.
What do you make of the table?

Prodigy.
We already knew that Jews achieve far beyond their numbers, but with a
mean IQ about one standard deviation higher than that of other Europeans,
we expect high achievement from them.

Mentor.
Can we bring something new ( if you'll forgive the expression) to the table,
something novel, perhaps a new insight? Can we find a pattern in the data
that will organize them in a meaningful way? Can we, for example, use the
data to predict something new -- something yet to be observed -- a logical
consequence of the pattern -- a prediction, verifiable, at least in principle?

Prodigy.
You mean like the predicted existence of W and Z particles that grew out
of the unified theory of weak and electromagnetic forces?

Mentor.
An excellent example, though I had something less grand in mind. As you
know Salam and Weinberg proposed W and Z in 1967, but not until 1983 were
the particles observed. Incidentally, since Steven Weinberg won a Nobel Prize for
the electroweak theory, he is no doubt represented in the percentage of
Jewish Nobel laureates found in Hu's data. Do you think the same qualities
that enable Jews to win Nobel prizes also equip them to hold top Hollywood
positions?

Prodigy.
The hallmark of the Ashkenazic Jew is intelligence. We know that intelligence
correlates with many kinds of achievement, so it is not terribly surprising
to find Jews disproportionately winning Nobel Prizes and also making movies.

Mentor.
But surely some of the categories are more demanding of intellect than
others. Which of them do you associate most closely with high IQ?

Prodigy.
Well certainly not California Senators. Nobel Prize winners come immediately
to mind, but also faculty at elite colleges, Ivy leaguers, Westinghouse
winners, Supreme Court law clerks, MacArthur and ACM Turing Award winners.
They all seem good bets for high IQs.

Mentor.
Would you consider acceptance to the Ivy league and winning a Nobel Prize
comparable intellectual feats?

Prodigy.
Both groups are extremely bright. Based on SAT scores, Ivy Leaguers are
far out on the right-hand tail of the bell curve. And keep in mind the
Ivy League SAT scores are diluted by "legacy" admits, athletic scholarship
winners, and minority affirmative action admissions.

Mentor.
Why do you include Supreme Court law clerks?

Prodigy.
They are mostly the best graduates of the best law schools. They have passed
through a double screen, having survived a keen competition to be admitted
to a premier law school, and then to have risen to the top of that group.

".
. . if you are looking for an antiseptic link to intelligence, the MacArthur
grantees will not do."

Mentor.
What about the MacArthur winners?

Prodigy.
The MacArthurs are after all "genius" grants.

Mentor.
Consider this. In 1999 there were 32 MacArthur winners. Fifteen were women.
In the annals of human accomplishment, there is no precedent for that kind
of female representation. Most of the recipients also have a distinctly
left-wing flavor to their work. Others are positive flakes. Citations for
the awards include phrases like "leader in the struggle for human rights
in southern Africa," "scholar of race relations," "a strong socio-political
sensibility in her works" etc. One of the 1995 geniuses, the feminist musicologist
Susan McClary is described in the award announcement as "a musicologist
who explores the relationship between human experiences and music and relates
the creation of musical works to their social context." One of her major
discoveries is that classical music is full of phallic themes. John Leo
writing in U.S. News and World Report, observed "A lot of the [MacArthur]
award winners are either ideologues . . . or low-luster laborers in the
traditional vineyards of the left." I am afraid, Prodigy, that if you are
looking for an antiseptic link to intelligence, the MacArthur grantees
will not do.

Prodigy.
OK so we'll scratch the "geniuses." I also have a problem with the Nobel
laureates in the table. The Jews represented in the table are primarily
American Jews, whereas the Nobel laureates come from all over. There is
a certain incompatibility. We should be looking at American Jews there
too, so with your permission I will substitute the percentage of American
Nobelists who are Jewish. The number is 27 percent.

Mentor.
Well, let's see what the table looks like after selecting the areas with
the most obvious links to IQ.

% Jewish

20-30%

Westinghouse Science
Prize

30%

Faculty at elite colleges

30%

Supreme Court Law Clerks

27%

Ivy Leaguers

25%

ACM Turing Award

27%

Nobel Prizes won by
Americans

Prodigy.
The average in the six surviving categories is 27 percent Jewish, with
a spread that looks like a thin film. I suggest a generalization: American
Jews will constitute about 27 percent of any group whose distinguishing
characteristic is intelligence. Can we call this Prodigy's conjecture?

Mentor.
If you like, but I do have some questions.

Prodigy.
Oops.

Mentor.
As we continue out along the right tail of the bell curve, the highest
IQ group will be increasingly represented. Since the faculty of elite colleges
as well as supreme court clerks have a greater percentage of Jews (30)
than the Nobel laureates (27), can we infer that these professors and law
clerks are brighter on average than Nobel laureates?

Prodigy.
The professors, law clerks and Nobel laureates are all so highly selected
that distinguishing among them with respect to IQ is difficult. A more
likely explanation is that in this context, 27 = 30.

Mentor.
How about a prediction based on your conjecture?

Prodigy.
Let me think for a moment. We know the percentage of Jews in the high IQ
areas, i.e., 27%, and also their percentage in the general population.
In addition, we know that the mean Jewish IQ is about one standard deviation
above that of other European types. From this I will estimate the mean
IQ of the Nobel laureates.

Mentor.
And how exactly will you do that?

Prodigy.
Let's define a few quantities: NJ is the number of Jews
in the U.S.; NE is the corresponding number of non-Jews
of European ancestry; P is the normalized probability distribution
(assumed Gaussian) of IQ among non-Jewish European types; λ
is the IQ of the Nobelist with the lowest IQ, the bottom of his class so
to speak; fJ is the fraction of Jews among the Nobelists,
i.e., 0.27, which we also assume to be the fraction of Jews in the general
population with IQ's at or above λ;
finally, Δ
is the difference in mean IQ (European - Jewish), i.e., -1.0. We may then
write:

where in (1) we have used the following
transformation:

Equation (1) is
more conveniently written in terms of the ratio, NJ /NE,
i.e.,

Prodigy.
Thank you. Using this value and setting fJ =0.27, and
Δ = -1.0,
we can solve (3) numerically for λ.
One moment please . . . I get a value of 2.60 for λ.
That is, if 15 IQ points is one standard deviation, then the dimmest bulb
among the laureates has an IQ of 139.

Mentor.
What about their average IQ?

Prodigy.
There are several averages we can compute, the average IQ of the Jewish
Nobelists, the non-Jewish Nobelists, and all the Nobelists.

Mentor.
Shouldn't they all be the same?

Prodigy.
Not really. The Jewish Nobelists will have the highest average IQ, because
as we move out along the right-hand tail of the distribution curves, on
past the dimmest bulb threshold, the Jewish distribution becomes ever more
dominant. Remember, at the threshold Jews are 1.60 standard deviation beyond
their mean, while the non-Jews are 2.60 SD out from their
mean.

We can compute
the Jewish average, < IQJ > as:

The denominator
in (4) re-normalizes the distribution for Jews. In the numerator we have
used the transformation,

Doing the arithmetic,
we find: < IQJ > = 3.02 or 145.3 IQ points. That is,
to 3 figures we predict the average IQ of the Jewish laureates to be 145.

The average IQ
of the non-Jewish Nobelists, < IQE >, is simply

Doing the arithmetic
here gives: < IQE > = 2.91 or 143.7 IQ units. To 3
figures we estimate the average IQ of the non-Jewish laureates as 144,
1 point lower than that of the Jews. Sparing you the obvious arithmetic,
we estimate the average IQ of the laureates overall to be 144.2 or simply
144, the same as the non-Jewish average.

Mentor.
I asked earlier if professors at elite universities and Supreme Court law
clerks are brighter than Nobel laureates since the Jewish presence is a
bit greater in these areas, i.e., 30% vs. 27%. You answered to the effect
that for our purposes, 27 = 30. What happens if you plug 30 percent into
your engine instead of 27?

Prodigy.
Just a moment while I do the computation . . . A 30 percent Jewish presence
yields an overall average IQ of 146 instead of 144. Not a great difference
would you say? It seems my 27 = 30 statement is more or less justified,
a two point IQ difference being well within the error of my analysis, not
to mention the state of the psychometric art.

Mentor.
I must say I am impressed.

Prodigy.
Do you recall a Problem for the Heterodox posed by La Griffe du
Lion that asked for an estimate of the average IQ of the Nobel laureates?
Do you think my solution will be satisfactory? Will I be eligible for a
prize?

Mentor.
You may be eligible for a prize. La Griffe has been known occasionally
to award cigars, but that will have to wait until you grow up.